Abstract
We introduce an algorithm for Additive Schur Complement Approximation (ASCA) that can be used in various iterative methods for solving systems of linear algebraic equations arising from finite element discretization of Partial Differential Equations (PDE). Here we consider a model problem of a scalar elliptic PDE with highly oscillatory (piecewise constant) diffusion coefficient. The main ideas are illustrated by three different examples that reveal the key point of constructing a robust sparse ASCA. We also demonstrate how the quality of the ASCA can be improved and how its sparsity is controlled.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Axelsson, O., Blaheta, R., Neytcheva, M.: Preconditioning of boundary value problems using elementwise Schur complements. SIAM J. Matrix Anal. Appl. 31, 767–789 (2009)
Kraus, J.: Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Numer. Linear Algebra Appl. 13, 49–70 (2006)
Neytcheva, M., Do-Quang, M., Xin, H.: Element-by-Element Schur Complement Approximations for General Nonsymmetric Matrices of Two-by-Two Block Form. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 108–115. Springer, Heidelberg (2010)
Neytcheva, M.: On element-by-element Schur complement approximations. Linear Algebra and Its Applications 434, 2308–2324 (2011)
Scheichl, R., Vassilevski, P., Zikatanov, L.: Weak approximation properties of elliptic projections with functional constraints, Tech. report, LLNL (February 2011) (submitted to Multiscale Modeling & Simulation)
Vassilevski, P.: Multilevel Block Factorization Preconditioners. Springer, New York (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kraus, J. (2012). Additive Schur Complement Approximation for Elliptic Problems with Oscillatory Coefficients. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-29843-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29842-4
Online ISBN: 978-3-642-29843-1
eBook Packages: Computer ScienceComputer Science (R0)